Beyond r*: A financial conditions neutral rate
In this paper Ricardo J. Caballero, Tomas E. Caravello, and Alp Simsek make the argument that r* is contaminated by financial fluctuations (risk premia, sentiment), so a better benchmark for the monetary policy stance is Financial Conditions Index FCI*, the neutral level of a financial conditions index.
What is FCI*
- FCI* is defined as the neutral level of a Financial Conditions Index (specifically the Fed’s FCI-G index) consistent with output at potential .
- Because financial conditions already incorporate the demand effects of asset prices, those effects do not need to be absorbed by the neutral benchmark, FCI* is therefore insulated from financial fluctuations and driven only by macroeconomic forces (trend growth, supply shocks, demand shocks) .
Methodology
- The authors build a two-equation semi-structural model closely modelled on Laubach-Williams (2003), but replace the interest rate IS curve with an FCI-based IS curve where output gaps are linked to FCI gaps rather than real interest rate gaps .
- FCI* is treated as a latent state variable and estimated via the Kalman filter using quarterly U.S. data from 1990Q2 to 2024Q4, with adjustments for the COVID-19 period via the Oxford Stringency Index .
- Phillips curve parameters are fixed to Holston et al. (2023) values to ensure that any differences in results stem from the demand block specification, not the inflation equation .
Key empirical findings
1.FCI* does not correlate with the equity risk premium once macroeconomic conditions are controlled for. By contrast, standard r* remains strongly correlated with the risk premium even after controlling for output gaps .
2. The IS curve fits significantly better with FCI than with interest rates, yielding more stable estimates of the neutral benchmark .
3. FCI gaps tell a different story from r* gaps in key episodes:
- Post-GFC recovery (2010–2020): Standard r*-based gaps suggested policy was highly accommodative. FCI gaps instead showed financial conditions were roughly neutral or slightly tight, consistent with persistently negative output gaps and the “missing disinflation” puzzle .
- 2022 tightening cycle: FCI gaps captured the rapid tightening (via rising long-term yields and falling equity prices) well before interest rate gaps did, since asset prices moved ahead of policy rate hikes .
- 2023–2024: FCI gaps signaled a loosening driven by the equity market rally, even as policy rates remained high .
- FCI* closely tracks the optimal FCI target derived from a separate, structurally richer model (Caballero et al. 2024), validating it as a practical guide outside of crisis periods .
The paper proposes FCI* as a pragmatic, theoretically grounded alternative to r* for real-time policy stance assessment. It is especially valuable when financial conditions diverge from the policy rate, a situation that has become increasingly common given financial deepening and the growing role of market-based finance .
FCI-star
Authors: Ricardo J. Caballero, Tomas E. Caravello, Alp Simsek
From: MIT, Yale
Beyond r*: A macro-finance approach
This paper by Claus Brand, Gavin Goy, and Wolfgang Lemke tackles the same “natural rate puzzle” i.e. the disconnect between macro-based and finance-based r* estimates, but takes the opposite strategic approach than Caballero et al. above: rather than abandoning r*, the authors build a unified macro-finance yield curve model where r* simultaneously anchors both the output gap and the term structure. They find that longer-maturity real rate gaps (e.g., 10-year) explain output gaps better than short-term rate gaps, a finding that resonates with FCI*’s emphasis on broad financial conditions beyond the policy rate.
What the model does
- The authors introduce a unified macro-finance model where r* plays a dual role: (1) as the benchmark real rate that closes the output gap in the IS curve, and (2) as the time-varying long-run anchor for the entire nominal yield curve .
- The yield curve component is an arbitrage-free Nelson-Siegel (AFNS) term structure model where the level factor has a non-stationary trend pinned to the equilibrium nominal short rate , while slope and curvature factors are stationary .
- The macro component closely follows Holston, K., Laubach, T., and Williams, J. C., 2017 (HLW), with an IS curve linking output gaps to real rate gaps, a Phillips curve for inflation, and r* decomposed into potential output growth and a non-growth “catch-all” component .
Methodology
The model was estimated using Bayesian methods on quarterly U.S. data from 1961Q2 to 2019Q4 . Observables include: real GDP, CPI inflation, 13 nominal zero-coupon bond yields (1 quarter to 10 years), a long-run inflation expectations survey (Fed’s PTR series), and 1-year-ahead short-rate consensus forecasts .
Findings
- r* shows a rise-and-fall pattern over six decades — lower in the 1960s–70s and post-GFC than HLW suggests, rather than a monotonic decline — more consistent with the finance-based estimates of Bauer & Rudebusch (2020) .
- The real rate gap is stationary and cyclical in this model, in sharp contrast to HLW where it can drift persistently. This makes the policy stance assessment more plausible historically .
- Estimation uncertainty is substantially narrower: the 90% credible interval for r* averages 2.3 percentage points, versus 8 percentage points in HLW .
- All three data sources matter: macro data, yield curve data, and surveys all contribute meaningfully to identifying r*. Neither short nor long rates alone are sufficient .
- Long-term real rate gaps are preferred: a model comparison exercise finds that a 10-year real rate gap in the IS curve achieves the highest marginal likelihood, outperforming the standard short-term gap specification .
- Term premia are cyclical, not trending: by accounting for the secular decline in equilibrium rates, the expectations component absorbs the trend in long-term yields, leaving term premia stationary — in contrast to standard models that produce trending term premia .
By integrating macro stabilization logic with no-arbitrage yield curve discipline into a single coherent model, the paper resolves the disconnect between macro and finance estimates of r*, produces a more plausible and tighter-measured policy stance indicator, and shows that long-term interest rates, not just the short rate, carry important information about neutral monetary conditions .
Estimating the Natural Rate of Interest in a Macro-Finance Yield Curve Model
Authors: Claus Brand, Gavin Goy, Wolfgang Lemke
From: European Central Bank, De Nederlandsche Bank
